Abstract
The solution to the classic so-called Couplet’s problem was provided more than a century ago, and recently, in the frame of limit equilibrium analysis, elliptical and pointed arches have also been carried out. Albeit triangular form of arches is the structural precursor of the mentioned ones, its mechanical behaviour has not been sufficiently researched. Therefore, the present paper elaborates in detail the thrust line analysis of different types of triangular arches under self-weight. Hence, with respect to vertical, normal, horizontal and radial stereotomy, the closed-form expression of the corresponding thrust line, as well as the numerical values for the minimum thickness, is derived.
Similar content being viewed by others
References
Aita, D., Corradi, M.: On the equilibrium of the flat arch with joints that have neither friction nor cohesion. In: Becchi, A., Corradi, M., Foce, F., Pedemonte, O. (eds.) Towards a History of Construction, pp. 505–521. Birkhäuser, Basel (2002)
Alexakis, H., Makris, N.: Limit equilibrium analysis of masonry arches. Arch. Appl. Mech. 85(9), 1363–1381 (2015)
Alexakis, H., Makris, N.: Minimum thickness of elliptical masonry arches. Acta Mech. 224(12), 2977–2991 (2013)
Barlow, W.H.: On the Existence (practically) of the line of equal Horizontal Thrust in Arches, and the mode of determining it by Geometrical Construction. Minutes Proc. Inst. Civ. Eng. 5, 162–182 (1846)
Benvenuto, E.: An Introduction to the History of Structural Mechanics. Springer, New York (1991)
Cocchetti, G., Colasante, G., Rizzi, E.: On the analysis of minimum thickness in circular masonry arches. Appl. Mech. Rev. 64(5), 2011 (2011)
Coulomb, C.A.: Essai sur une application des régles des Maximis & Minimis à quelques Problémes de Statique, relativs a l’Arquitecture. Mémoires de Mathématique et de Physique, présentés à l’Académie Royal des Sciences per divers Savans, & lûs dans ses Assemblées 1, 343–382 (1773)
Couplet, P.: Seconde partie de l’examen de la poussée des voûtes. Histoire de l’Académie Royale des Sciences 117–141 (1730)
De la Hire, P.: Traité de mécanique. Imprimerie Royale, Paris (1695)
Foce, F.: Milankovitch’s Theorie der Druckkurven: good mechanics for masonry architecture. Nexus Netw. J. 9(2), 185–210 (2007)
Gaspar, O., Sipos, A.A., Sajtos, I.: Effect of stereotomy on the lower bound value of minimum thickness of semicircular masonry arches. Int. J. Archit. Herit. 12(6), 899–921 (2018)
Gerstner, F.J.R.: Handbuch der Mechanik. Johann Spurny, Buchdrucker und Schriftgiesser, Prag (1831)
Heyman, J.: Coulomb’s Memoir on Statics: An Essay in the History of Civil Engineering. Cambridge University Press, Cambridge (1972)
Heyman, J.: The Stone Skeleton: Structural Engineering of Masonry Architecture. Cambridge University Press, Cambridge (1997)
Huerta, S.: Wedges and plate-bandes: mechanical theories after De la Hire. In: Gargiani, R. (ed.) L’architrave, le plancher, la plate-forme. Nouvelle Histoire de la construction. Architecture Essais, pp. 405–435. Presses polytechniques et universitaires romandes, Lausanne (2012)
Kurrer, K.E.: The History of the Theory of Structures: Searching for Equilibrium, vol. 2. Wilhelm Ernst & Sohn Verlag für Architectur und technische Wissenschaften GmbH & Co. KG, Berlin (2018)
Makris, N., Alexakis, H.: The effect of stereotomy on the shape of the thrust-line and the minimum thickness of semicircular masonry arches. Arch. Appl. Mech. 83(10), 1511–1533 (2013)
Méry, E.: Sur l’équilibre des voûtes en berceau. Annales des Ponts et Chaussées 1(1), pl. CLXXIII and CLXXXIV, 50–70 (1840)
Milankovitch, M.: Theorie der Druckkurven. Zeitschrift für Mathematik und Physik 55, 1–27 (1907)
Milankovitch, M.: Zur Statik der massiven Widerlager. Zeitschrift für Mathematik und Physik 58, 120–128 (1910)
Moseley, H.: The Mechanical Principles of Engineering and Architecture, London (1843)
Nikolić, D.: Thrust line analysis and the minimum thickness of pointed masonry arches. Acta Mech. 228(6), 2219–2236 (2017)
Nikolić, D.: A note on the equilibrium analysis of inclined plate-bande. In: Proceedings of the 5th International Conference Contemporary Achievements in Civil Engineering, Faculty of Civil Engineering Subotica, pp. 393–392 (2017)
Nikolić, D.: Catenary arch of finite thickness as the optimal arch shape. Struct. Multidiscip. Optim. 60, 1957–1966 (2019). https://doi.org/10.1007/s00158-019-02304-9
Nikolić, D., Štulić, R.: Equilibrium analysis of frictionless triangular arches: geometrical formulation. FME Trans. 45(2), 307–313 (2017)
Young, T.: [signed Apsophus]: Remarks on the structure of covered ways, independent of the principle of the arch in equilibrium, and on the best forms for arches in buildings. J. Nat. Philos. Chem. Arts 18, 241–250 (1807)
Young, T.: Bridge. Supplement to the fourth, fifth and sixth editions of the Encyclopaedia Britannica, vol. 2, pp. 497–520, pl. 42–44. Archibald Constable, Edinburgh (1824)
Acknowledgements
The paper was done within the Project No. TR36042 supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Nikolich, D. Thrust line analysis of triangular arches. Arch Appl Mech 90, 1861–1874 (2020). https://doi.org/10.1007/s00419-020-01701-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-020-01701-7